## Abstract

A sensitive differential method is described for isolating from other losses the residual reflectivity of an antireflection coating deposited on a quarterwave plate. Insertion of such a plate into a passive cavity reveals two eigenstates related to its axis, which may be by nature simultaneously resonant and antiresonant. The ratio between the two corresponding output intensities depends on the residual reflectivity of the plate and is moreover enhanced by the resonator. A residual reflectivity resolution of 10 ppm with a relatively low cavity finesse of 70 is achieved, and the possibility of measuring separately the losses from the coating and the substrate, using a half-coated quarterwave plate, is developed. We discuss the performances of our experimental setup and possible improvements and extensions of the method, in particular to isotropic components.

© 1988 Optical Society of America

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### Equations (14)

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(1)
$${T}_{r}=\frac{{T}_{p}^{2}(1-{A}_{s})}{{[1-{R}_{p}(1-{A}_{s})]}^{2}},$$
(2)
$${T}_{a}=\frac{{T}_{p}^{2}(1-{A}_{s})}{{[1+{R}_{p}(1-{A}_{s})]}^{2}}.$$
(3)
$${T}_{p}+{R}_{p}+{A}_{p}=1,$$
(4)
$${T}_{r}\simeq 1-2{A}_{p}-{A}_{s},$$
(5)
$${T}_{a}\simeq {T}_{r}-4{R}_{p}.$$
(6)
$${K}_{r}/{K}_{a}={T}_{r}/{T}_{a}\xb7{\left(\frac{1-R\xb7{T}_{a}}{1-R\xb7{T}_{r}}\right)}^{2},$$
(7)
$${K}_{r}/{K}_{a}\simeq {\left(1+\frac{4R\xb7{R}_{p}}{1-R\xb7{T}_{r}}\right)}^{2}.$$
(8)
$${F}_{r}=\pi \xb7\frac{{(R\xb7{T}_{r})}^{1/2}}{(1-R\xb7{T}_{r})}.$$
(9)
$${K}_{r}/{K}_{a}\simeq {\left(1+\frac{4}{\pi}\xb7{F}_{r}\xb7{R}_{p}\right)}^{2}.$$
(10)
$${R}_{p}\simeq \frac{\pi}{4\xb7{F}_{r}}[{({K}_{r}/{K}_{a})}^{1/2}-1].$$
(11)
$${K}_{r}/{K}_{a}={\left(\frac{{K}_{r1}\xb7{K}_{r2}}{{K}_{a2}\xb7{K}_{a1}}\right)}^{1/2}$$
(12)
$${T}_{r}^{u}\simeq 1-{A}_{s},$$
(13)
$${A}_{p}\simeq \frac{\pi}{2\xb7{F}_{r}^{u}}[{({K}_{r}^{u}/{K}_{r})}^{1/2}-1],$$
(14)
$${A}_{s}\simeq \frac{\pi}{F}[{(K/2{K}_{r}^{u})}^{1/2}-1],$$